Question

How would you describe the following events given a standard deck of cards?

Event A: Drawing a red card

Event B: Drawing a card with a number

Question 11 options:

Independent


Mutually Exclusive


Inclusive


Conditional

Answer 1

To analyze the relationship between Event A (drawing a red card) and Event B (drawing a card with a number) in the context of a standard deck of cards, let's break down the events:

- **Event A (Drawing a red card):** A standard deck has 52 cards, 26 of which are red (13 hearts and 13 diamonds).

- **Event B (Drawing a card with a number):** In a standard deck, the numbered cards range from 2 to 10 in each suit, giving us a total of 36 cards with numbers (9 numbered cards in each of the 4 suits).

Now, let's evaluate the relationship between these events:

1. **Independent:** Two events are independent if the occurrence of one does not affect the occurrence of the other. In this case, knowing that you drew a red card does not provide any information that would affect the probability of drawing a card with a number.

2. **Mutually Exclusive:** Two events are mutually exclusive if they cannot happen at the same time. In this case, one can draw a red card that is also a number (e.g., 2 of hearts or 8 of diamonds). Therefore, the two events are not mutually exclusive.

3. **Inclusive:** This term generally refers to events that can happen simultaneously, which is related to the understanding of overlap. Since they can occur together (drawing a red numbered card), one could see some inclusivity here.

4. **Conditional:** This term applies when one event's occurrence affects the probability of another. These events are not conditional upon each other since drawing a red card does not change the probability of drawing a numbered card.

Given this analysis, the best answer would be that Event A and Event B are **Independent** since knowing that one occurs doesn't provide information about the occurrence of the other.